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Simplifying 1.6x2 + -10.0x + 6.2 = 0 Reorder the terms: 6.2 + -10.0x + 1.6x2 = 0 Solving 6.2 + -10.0x + 1.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. 3.875 + -6.25x + x2 = 0 Move the constant term to the right: Add '-3.875' to each side of the equation. 3.875 + -6.25x + -3.875 + x2 = 0 + -3.875 Reorder the terms: 3.875 + -3.875 + -6.25x + x2 = 0 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + -6.25x + x2 = 0 + -3.875 -6.25x + x2 = 0 + -3.875 Combine like terms: 0 + -3.875 = -3.875 -6.25x + x2 = -3.875 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -3.875 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -3.875 + 9.765625 Combine like terms: -3.875 + 9.765625 = 5.890625 9.765625 + -6.25x + x2 = 5.890625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + -3.125) equal to 2.42706098 and -2.42706098.Subproblem 1
x + -3.125 = 2.42706098 Simplifying x + -3.125 = 2.42706098 Reorder the terms: -3.125 + x = 2.42706098 Solving -3.125 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.42706098 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.42706098 + 3.125 x = 2.42706098 + 3.125 Combine like terms: 2.42706098 + 3.125 = 5.55206098 x = 5.55206098 Simplifying x = 5.55206098Subproblem 2
x + -3.125 = -2.42706098 Simplifying x + -3.125 = -2.42706098 Reorder the terms: -3.125 + x = -2.42706098 Solving -3.125 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.42706098 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.42706098 + 3.125 x = -2.42706098 + 3.125 Combine like terms: -2.42706098 + 3.125 = 0.69793902 x = 0.69793902 Simplifying x = 0.69793902Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.55206098, 0.69793902}
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